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2 years ago

6

Write the EQ of circle i find center and radius given x² + y²-4x+12y =-4

2 answers:

rusak2 [61]2 years ago

3 0

Answer:

CENTER :(2,-6)

RADIUS: 6

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belka [17]2 years ago

3 0

Step-by-step explanation:

Hey there!

Given;

${x}^{2} + {y}^{2} - 4x + 12y = \: - 4$

Now, Try to make it a perfect square.

${x}^{2} - 4x + {(2)}^{2} - ( { 2)}^{2} + {y}^{2} + 12y + ( {6)}^{2} - ( {6)}^{2} = - 4$

Make perfect square and shift -(2)^2 and -(6)^2 on right side.

$( {x - 2)}^{2} ( {y + 6)}^{2} = - 4 + 40$

$( {x - 2)}^{2} ( {y + 6)}^{2} = 36$

Comparing the equation with (x-h)^2(y-h)^2= r^2.

We get,

Centre (h,k)= (2,-6)

Radius (r) = 6

<em><u>Hop</u></em><em><u>e</u></em><em><u> </u></em><em><u>it</u></em><em><u> helps</u></em><em><u>.</u></em><em><u>.</u></em><em><u>.</u></em>

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A pasture is twice as long as it is wide. its area is 88,200 ft2. how wide is the pasture?

OLga [1]

If the width is w and the length is l, then 2w=l. In addition, l*w=88200 (using the area formula). Plugging 2w in for l, we get 2w*w=88200=2w^2. Dividing both sides by 2, we get w^2=44100 and w=sqrt(44100)=210.

4 0

2 years ago

Find the solution set for this equation:<br> -a2+4a=0<br> (Separate the two values with a comma)

Rashid [163]

$\quad \huge \quad \quad \boxed{ \tt \:Answer }$

$\qquad \tt \rightarrow \: \{ 0,4 \}$

____________________________________

$\large \tt Solution \: :$

$\qquad \tt \rightarrow \: - {a}^{2} + 4a = 0$

$\qquad \tt \rightarrow \: - ( {a}^{2} - 4a) = 0$

$\qquad \tt \rightarrow \: {a}^{2} - 4a = 0$

$\qquad \tt \rightarrow \:a(a - 4) = 0$

The two cases are :

a = 0

or

a -4 = 0, that leads to a = 4

We can conclude :

$\qquad \tt \rightarrow \:solution \: (a) = \{ 0,4\}$

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

5 0

1 year ago

Read 2 more answers

What is the equation of the best-fitting regression line? Find this in two ways. First, using the regression analysis part of th

Lemur [1.5K]

Step-by-step explanation:

Regression analysis is used to infer about the relationship between two or more variables.

The line of best fit is a straight line representing the regression equation on a scatter plot. The may pass through either some point or all points or none of the points.

<u>Method 1:</u>

Using regression analysis the line of best fit is: $y=\alpha +\beta x+e$

Here <em>α </em>= intercept, <em>β</em> = slope and <em>e</em> = error.

The formula to compute the intercept is:

$\alpha =\bar y-\beta \bar x$

Here<em> </em> $\bar y$ and $\bar x$ are mean of the <em>y</em> and <em>x</em> values respectively.

$\bar y=\frac{\sum y_{i}}{n} \\\bar x=\frac{\sum x_{i}}{n}$

The formula to compute the slope is:

$\beta =\frac{\sum (x-\bar x)(y - \bar y)}{\sum (x=\bar x)^{2}}$

And the formula to compute the error is:

$e=y-\alpha -\beta x$

<u>Method 2:</u>

The regression line can be determined using the descriptive statistics mean, standard deviation and correlation.

The equation of the line of best fit is:

$(y-\bar y)=r\frac{\sigma_{x}}{\sigma_{y}} (x-\bar x)$

Here <em>r</em> = correlation coefficient = $r=\frac{Cov (x,y)}{\sqrt{\sigma^{2}_{x}\sigma^{2}_{y}} }$

$\sigma_{x}$ and $\sigma_{y}$ are standard deviation of <em>x</em> and <em>y</em> respectively.

$\sigma_{x}=\frac{1}{n}\sum (x-\bar x)^{2} \\\sigma_{y}=\frac{1}{n}\sum (y-\bar y)^{2}$

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3 years ago

9. A boy rides away from home in an automobile at the rate of 28 miles an hour and walks back at the rate of 4 miles an hour. Th

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Answer:

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2 years ago

the time required to assemble computers varies directly as the number of computers assembled and inversely as the number of work

olga2289 [7]

Answer:

16 hours

Step-by-step explanation:

let t be time, n the number of computers and w the number of workers, then

t = $\frac{kn}{w}$ ← k is the constant of variation

To find k use the condition n = 30, w = 6 and t = 10 , then

10 = $\frac{30k}{6}$ ( multiply both sides by 6 )

60 = 30k ( divide both sides by 30 )

2 = k

t = $\frac{2n}{w}$ ← equation of variation

When w = 5 and n = 40 , then

t = $\frac{2(40)}{5}$ = $\frac{80}{5}$ = 16 hours

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2 years ago